Use the given row transformation to change the matrix as indicated.
-$\left[ \begin{array} { r r r } 3 & 5 & 12 \ 2 & 1 & 2 \ 4 & - 1 & 4 \end{array} \right] ; - 2$ times row 2 added to row 3
A)
$\left[ \begin{array} { r r r } 3 & 5 & 12 \ 2 & 1 & 2 \ 8 & 1 & 8 \end{array} \right]$
B)
$\left[ \begin{array} { r r r } 3 & 5 & 12 \ 2 & 1 & 2 \ 0 & - 2 & 2 \end{array} \right]$
C)
$\left[ \begin{array} { r r r } 3 & 5 & 12 \ 2 & 1 & 2 \ 0 & - 3 & 0 \end{array} \right]$
D)
$\left[ \begin{array} { r r r } - 1 & 3 & 8 \ 2 & 1 & 2 \ 4 & - 1 & 4 \end{array} \right]$

Question

Quizplus · Accepted Answer

To apply the transformation, we multiply each element of row 2 by -2 and add the result to the corresponding element of row 3. For row 3, the calculations are as follows: $4 + (-2 \times 2) = 4 - 4 = 0$, $(-1) + (-2 \times 1) = -1 - 2 = -3$, and $4 + (-2 \times 2) = 4 - 4 = 0$. This results in the new row 3 being $0, -3, 0$, which matches option C.

Use the Given Row Transformation to Change the Matrix as Indicated